Search results

The purpose of this paper is to find an exact analytical expression for the periodic solutions of the double-hump Duffing equation and an expression for the period of these solutions.

The double-hump Duffing equation is presented as a Hamiltonian system and a phase portrait of this system has been found. On the ground of analytical calculations performed using Hamiltonian-based technique, the periodic solutions of this system are represented by Jacobi elliptic functions sn, cn and dn.

Expressions for the periodic solutions and their periods of the double-hump Duffing equation have been found. An expression for the solution, in the time domain, corresponding to the heteroclinic trajectory has also been found. An important element in various applications is the relationship obtained between constant Hamiltonian levels and the elliptic modulus of the elliptic functions.

The results obtained in this paper represent a generalization and improvement of the existing ones. They can find various applications, such as analysis of limit cycles in perturbed Duffing equation, analysis of damped and forced Duffing equation, analysis of nonlinear resonance and analysis of coupled Duffing equations.

The purpose of this paper is to analyze the dynamical state of a discrete time engineering/physical dynamic system. The analysis is performed based on observability, controllability and stability first using difference equations of generalized motion obtained through discrete time equations of dissipative generalized motion derived from discrete Lagrange-dissipative model [{L,D}-model] for short of a discrete time observed dynamic system. As a next step, the same system has also been analyzed related to observability, controllability and stability concepts but this time using discrete dissipative canonical equations derived from a discrete Hamiltonian system together with discrete generalized velocity proportional Rayleigh dissipation function. The methods have been applied to a coupled (electromechanical) example in different formulation types.

An observability, controllability and stability analysis of a discrete time observed dynamic system using discrete equations of generalized motion obtained through discrete {L,D}-model and discrete dissipative canonical equations obtained through discrete Hamiltonian together with discrete generalized velocity proportional Rayleigh dissipation function.

The related analysis can be carried out easily depending on the values of classical elements.

Discrete equations of generalized motion and discrete dissipative canonical equations obtained by discrete Lagrangian and discrete Hamiltonian, respectively, together with velocity proportional discrete dissipative function are used to analyze a discrete time observed engineering system by means of observability, controllability and stability using state variable theory and in the method proposed, the physical quantities do not need to be converted one to another.

Wind turbines are of growing importance for the production of renewable energy. The kinetic energy of the blowing air induces a rotary motion and is thus converted into electricity. From the mechanical point of view the complex dynamics of wind turbines become a matter of interest for structural optimization and optimal control in order to improve stability and energy efficiency. The purpose of this paper therefore is to present a mechanical model of a three‐blade wind turbine with a momentum and energy conserving time integration of the system.

The authors present a mechanical model based upon a rotationless formulation of rigid body dynamics coupled with flexible components. The resulting set of differential‐algebraic equations will be solved by using energy‐consistent time‐stepping schemes. Rigid and orthotropic‐elastic body models of a wind turbine show the robustness and accuracy of these schemes for the relevant problem.

Numerical studies prove that physically consistent time‐stepping schemes provide reliable results, especially for hybrid wind turbine models.

The application of energy‐consistent methods for time discretization is intended to provide computational robustness and to reduce the computational costs of the dynamical wind turbine systems. The model is aimed to give a first access into the investigation of fluid‐structure interaction for wind turbines.

The purpose of this paper is to devise a new approach to synthesize closed‐loop feedback guidance law for online thrust‐insensitive optimal trajectory generation utilizing neural networks.

The proposed methodology utilizes an open‐loop variational formulation that initially determines optimal launch/ascent trajectories for various scenarios of known uncertainties in the thrust profile of typical solid propellant engines. These open‐loop optimized trajectories will then provide the knowledge base needed for the subsequent training of a neural network. The trained network could eventually produce thrust‐insensitive closed‐loop optimal guidance laws and trajectories in flight.

The proposed neuro‐optimal guidance scheme is effective for online closed‐loop optimal path planning through some measurable and computable engine and flight parameters.

Determination of closed‐loop optimal guidance law for non‐linear dynamic systems with uncertainties in system and environment has been a challenge for researchers and engineers for many years. The problem of steering a solid propellant driven vehicle is one of these challenges. Even though a few researchers have worked in the area of non‐linear optimal control and thrust‐insensitive guidance, this paper proposes a new strategy for the determination of closed‐loop online thrust insensitive guidance laws leading to optimal flight trajectories for solid propellant launch and ascent vehicles.

The use of software is overpowering our modern society. Advancement in technology is directly proportional to an increase in user demand which further leads to an increase in the burden on software firms to develop high-quality and reliable software. To meet the demands, software firms need to upgrade existing versions. The upgrade process of software may lead to additional faults in successive versions of the software. The faults that remain undetected in the previous version are passed on to the new release. As this process is complicated and time-consuming, it is important for firms to allocate resources optimally during the testing phase of software development life cycle (SDLC). Resource allocation task becomes more challenging when the testing is carried out in a dynamic nature.

The model presented in this paper explains the methodology to estimate the testing efforts in a dynamic environment with the assumption that debugging cost corresponding to each release follows learning curve phenomenon. We have used optimal control theoretic approach to find the optimal policies and genetic algorithm to estimate the testing effort. Further, numerical illustration has been given to validate the applicability of the proposed model using a real-life software failure data set.

The paper yields several substantive insights for software managers. The study shows that estimated testing efforts as well as the faults detected for both the releases are closer to the real data set.

We have proposed a dynamic resource allocation model for multirelease of software with the objective to minimize the total testing cost using the flexible software reliability growth model (SRGM).

Combining the characteristic of satellite “minisize nucleus” non‐equilibrium molecular dynamics (NEMD) method is used. We select corresponding Tersoff potential energy function to build model and, respectively, simulate thermal conductivities of silicon nanometer thin film.

NEMD method is used, and the corresponding Tersoff potential energy function is used to build model.

The thermal conductivities of silicon nanometer thin film are markedly below the corresponding thermal conductivities of their crystals under identical temperature. The thermal conductivities are rising with the increase of thickness of thin film; what's more, the conductivities have a linear approximation with thickness of the thin film.

It is difficult to do physics experiment.

The findings have some theory guidance to analyze satellite thermal control.

The calculation results of thermal conductivities specify distinct size effect. The normal direction thick film thermal conductivity of silicon crystal declines with the increasing temperature. The thermal conductivities are rising with the increase of thickness of thin film; what's more, the conductivities have a linear approximation with thickness of the thin film.

A theory of knowledge shows that all four systems of nature are recursive combinatorial‐hamiltonian self‐programmed flow‐wave systems that can be deduced from the usual Conservation Law promoted to the Axiom of Science.

The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete.

The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well.

Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented.

The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.